People say that I should “chomp on hanging pieces”… how do I do that?

First game I looked at. Move 15. Free pawn on d4 up for grabs. Your knight can jump in and gain tempo on the queen. Also possibly setting up a knight fork against the King and Rook. You missed it. On move 16 you moved your knight instead of defending it, thus setting up a situation where you hung your rook. Which amazingly, your opponent didn't take. Move 23 you blundered playing Qc7. Your opponent needed to find Rc1 and you would have been forced to give up your rook. So I think from this game there's definitely hanging pieces and blunders on both sides.

Here's another game you played.

Move 6 of this game you hang your knight by playing Nd4. You might not see that you hung it, but if your opponent had found Bc5 in response, pinning it to your queen, the knight is toast. You could try to defend it with c3, but your opponent could play e5 and that would be that. Later in the game, bro gifts you with Rxf3 on move 26. Very nice of your opponent. But then on move 29 you played Rc7 and straight up hung your Rook. 
Anyway. Looking at those two games (the most recent rapid games), there were definitely hanging pieces and lack of tactical awareness on both sides. Which is fine! You'll get there! I guess the last thing I'd mentioned is that you also want to be aware of pieces that have only one defender, because if you are able to remove the defender, the piece will hang. Also, overloaded pieces - this oftentimes occurs when a queen is protecting two pieces.

Good luck!

I think the trouble is that a "hanging" piece can sometimes be "poisoned," meaning it would be a terrible mistake to capture it.

For example: